Question

write the standard form of point -slope form of the straight line and find the equation of the straight line passing through the point (5,6) and slope of 3 units.​

Answer 1

Given,

The coordinate of the point$\[ = \left( {5,6} \right)\]$

The slope of the line$\[ = 3\]$

To find,

The equation of the line.

Solution,

Know that the standard form of point-slope form is $\[Ax + By = C\]$ where A is a positive integer and B and C are integers.

In the given question the points are $\[\left( {5,6} \right)\]$ and the slope of the line is $\[3.\]$

Therefore,

$\[\begin{array}{l} \Rightarrow \left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right)\\ \Rightarrow \left( {y - 6} \right) = 3\left( {x - 5} \right)\\ \Rightarrow y - 6 = 3x - 15\end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow 3x - 15 - y + 6 = 0\\ \Rightarrow 3x - y - 9 = 0\end{array}\]$

Hence, the equation of the line is$\[3x - y - 9 = 0\]$.